A004941 -id:A004941 - cp's OEIS frontend

A004942 a(n) = round(n*phi^7), where phi is the golden ratio, A001622.

0, 29, 58, 87, 116, 145, 174, 203, 232, 261, 290, 319, 348, 377, 406, 436, 465, 494, 523, 552, 581, 610, 639, 668, 697, 726, 755, 784, 813, 842, 871, 900, 929, 958, 987, 1016, 1045, 1074, 1103, 1132, 1161, 1190, 1219, 1248, 1278, 1307, 1336, 1365, 1394, 1423, 1452, 1481, 1510, 1539, 1568, 1597, 1626, 1655, 1684

Offset: 0

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A001622, A004939, A004940, A004941, A004943.

Table[Round[n GoldenRatio^7], {n, 0, 100}] (* Vincenzo Librandi, Oct 21 2014 *)

ph=(1+sqrt(5))/2; a(n)=round(n*ph^7);
vector(66,n,a(n-1)) \\ Joerg Arndt, Oct 21 2014

More terms from Joerg Arndt, Oct 21 2014

A004939 a(n) = round(n*phi^4), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 7, 14, 21, 27, 34, 41, 48, 55, 62, 69, 75, 82, 89, 96, 103, 110, 117, 123, 130, 137, 144, 151, 158, 164, 171, 178, 185, 192, 199, 206, 212, 219, 226, 233, 240, 247, 254, 260, 267, 274, 281, 288, 295, 302, 308

Offset: 0

N. J. A. Sloane

nonn

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A001622, A004940, A004941, A004942, A004943.

[Round(n*(7+3*Sqrt(5))/2): n in [0..80]]; // G. C. Greubel, Dec 04 2023

Round[Range[0,100]GoldenRatio^4] (* Paolo Xausa, Oct 28 2023 *)

[round(golden_ratio^4*n) for n in range(81)] # G. C. Greubel, Dec 04 2023

A004940 a(n) = round(n*phi^5), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 11, 22, 33, 44, 55, 67, 78, 89, 100, 111, 122, 133, 144, 155, 166, 177, 189, 200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 311, 322, 333, 344, 355, 366, 377, 388, 399, 410, 421, 433, 444, 455, 466, 477

Offset: 0

N. J. A. Sloane

nonn

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A001622, A004939, A004941, A004942, A004943.

[Round(n*(11+5*Sqrt(5))/2): n in [0..80]]; // G. C. Greubel, Dec 04 2023

With[{c=GoldenRatio^5},Round[c*Range[0,50]]] (* Harvey P. Dale, Nov 28 2021 *)

[round(golden_ratio^5*n) for n in range(81)] # G. C. Greubel, Dec 04 2023

A004943 a(n) = round(n*phi^8), where phi is the golden ratio, A001622.

Original entry on oeis.org

0, 47, 94, 141, 188, 235, 282, 329, 376, 423, 470, 517, 564, 611, 658, 705, 752, 799, 846, 893, 940, 987, 1034, 1081, 1127, 1174, 1221, 1268, 1315, 1362, 1409, 1456, 1503, 1550, 1597, 1644, 1691, 1738, 1785

Offset: 0

N. J. A. Sloane

nonn

a(n+48) - a(n+47) - a(n+1) + a(n) = 0 for 0 <= n <= 1055, but not for n = 1056. - Robert Israel, Oct 18 2023

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A001622, A004939, A004940, A004941, A004942.

p8:= simplify(((1+sqrt(5))/2)^8);
seq(round(n*p8),n=0..100); # Robert Israel, Oct 18 2023

Round[GoldenRatio^8 Range[0,40]] (* Harvey P. Dale, Sep 18 2023 *)

cp's OEIS Frontend

A004942 a(n) = round(n*phi^7), where phi is the golden ratio, A001622.

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A004939 a(n) = round(n*phi^4), where phi is the golden ratio, A001622.

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A004940 a(n) = round(n*phi^5), where phi is the golden ratio, A001622.

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Magma

Mathematica

SageMath

A004943 a(n) = round(n*phi^8), where phi is the golden ratio, A001622.

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